Numerical Tools Research Articles

Flow and Aeroacoustic Characteristics of Underexpanded Supersonic Jets Exhausting from a Conical Converging Nozzle

Ensuring the safety of space flights and solving the problems of reducing acoustic loads during the launch of space vehicles requires not only the development of new technical systems for launch complexes, but also methods for the numerical simulation of fluid and aeroacoustic fields generated by supersonic jets. The growing regulations for space vehicle noise also explain the interest in developing models and techniques that anticipate flow and the aeroacoustic characteristics of supersonic jets. Together with integral techniques for computing far-field noise, development of relevant mathematical models and implementation of numerical tools, the concepts of computational fluid dynamics (CFD) and computational aeroacoustics (CAA) are covered. The noise generated by a supersonic underexpanded jet is used to illustrate the capabilities of current numerical modelling and simulation tools. The jet structure, flow properties, and aeroacoustic quantities are affected by the nozzle pressure ratio. The outcomes of numerical simulation are contrasted with existing experimental and computational data. The available numerical modelling and simulation tools facilitate the development of novel computational methods and methodologies for challenges in CFD and CAA, in addition to solving research and engineering problems.

Utilizing Euler poles for the evaluation of plate rigidity in numerical mantle convection models

SUMMARY Evidence that the Earth’s surface is divided into a tessellation of piece-wise rigidly translating plates is the primary observation supporting the solid-state creep-enabled convection paradigm, utilized to investigate evolution of the Earth’s mantle. Accordingly, identifying the system properties that allow for obtaining dynamically generated plates remains a primary objective in numerical global mantle convection simulations. The first challenge for analysing fluid dynamic model output for the generation of rigid plates is to identify candidate plate boundaries. Here, we utilize a previously introduced numerical tool for plate boundary detection which uses a user specified threshold (tolerance) to automatically detect candidate plate boundaries. The numerical tool is applied with different sensitivities, to investigate the nature of the surface velocity fields generated in three calculations described in earlier work. The cases examined differ by the values that they specify for the model yield stress, a parameter that can allow the formation of tightly focussed bands of surface deformation. The three calculations we examine include zones comprising possible plate boundaries that are characterized by convergence, divergence and strike-slip behaviour. Importance of the potential plate boundaries is assessed by examining the rigidity of the inferred model generated plates. The rigidity is measured by comparing the model velocities to the rigid rotation velocities implied by the statistically determined Euler poles for each candidate plate. We quantify a lack in rigidity by calculating a deformity field based on disagreement of actual surface velocity with rotation about the Euler pole. For intermediate yield stress and boundary detection threshold value, we find that the majority of the model surface can translate almost rigidly about distinct plate Euler poles. Regions that conform poorly to large-scale region rigid translation are also obtained but we find that generally these regions can be decomposed into subsets of smaller plates with a lower tolerance value. Alternatively, these regions may represent diffuse boundary zones. To clarify the degree to which the mantle convection model behaviour shows analogues with Earth’s current-day surface motion, we apply the plate boundary detection and Euler pole calculation methods to previously published terrestrial strain-rate data. Strong parallels are found in the response of the terrestrial data and mantle convection calculations to the threshold value, such that appropriate choice of that parameter results in very good agreement between observations and convection model character. We conclude that plates generated by fluid dynamic convection models can exhibit motion that is markedly rigid, and define statistics (plateness) and fields (deformity) by which the generation of self-consistently determined plate rigidity can be quantified, as well as describing how plate recognition might be optimized. We also note that in agreement with the Earth’s current state, we obtain a dozen dominant plates in the case exhibiting the most plate-like (rigid) surface, suggesting that this approximate number of plates is perhaps intrinsic to the geometry, surface area and physical properties of Earth’s mantle.

Modelowanie numeryczne jako narzędzie do badania wybuchów wodoru

Currently, the burning of fossil fuels in industry or for transportation has a major negative impact on the environment. Most countries are concerned with environmental security and pollution regulation, motivating researchers around the world to find alternative solutions. An alternative solution may be the large-scale use of hydrogen. Applications of hydrogen in industry or for transportation face challenging conditions. Among other things, we are talking about pressures of up to 1000 bar, extreme temperatures starting from -253 °C (for liquefied hydrogen) and up to 650 °C - 950 °C (in the case of solid oxide electrolytic cells), as well as the imminent risk of explosion. This is because H2 has an extremely low ignition energy, with much wider flammability limits compared to other fuels such as methane or propane. Hydrogen is a highly reactive and explosive gas. Therefore, explosion protection is essential for all processes involving the use of hydrogen in one form or another. The same principles that are applied to natural gas can be applied. Hydrogen behaves similarly to methane in terms of explosion risk, meaning in principle that explosion protection works similarly for both gases. However, there are still many unknowns regarding the phenomenon of initiation and propagation of explosions caused by air-hydrogen mixtures. Taking into account the multiple aspects related to security techniques that must be taken into account for the use of hydrogen in industry or for transport, the current paper focuses on aspects with regard to the use of modern numerical modelling tools for increasing the occupational health and safety level in technological processes endangered by the occurrence of explosive atmospheres generated by air-hydrogen mixtures. It presents a review on the main research activities to be carried out within a the H2Model research project implemented between 2023 – 2026, project which focuses on numerical modelling on the ignition and propagation of explosions caused by air-hydrogen mixtures.

Using MODFLOW to Model Riparian Wetland Shallow Groundwater and Nutrient Dynamics in an Appalachian Watershed

Simulating shallow groundwater (SGW) flow dynamics and stream–SGW interactions using numerical modeling tools is necessary to develop a mechanistic understanding of water flow systems and improve confidence in water resource management practices. A three-dimensional (3D) SGW flow model was developed for a riparian wetland in a mixed forest and agricultural catchment in West Virginia (WV), Appalachia, USA, using a Modular 3D Groundwater Model (MODFLOW). The MODFLOW simulation was calibrated in steady (R2 = 0.98, ME = −0.21, and RMSE = 0.77), transient state (R2 = 0.97, ME = −0.41, and RMSE = 1.28) and validated (R2 = 0.97, ME = −0.28, and RMSE = 1.05) using observed SGW levels from thirteen nested piezometers under steady and transient states. An experimental MT3D transport scenario was developed to show the lateral transport of NO₃-N from the aquifer to stream cells. Relatively stable SGW head distribution was observed. In the downstream reach, SGW discharge varied from 948 m3/day to 907 m3/day in 2020, with creek seepage ranging from 802 m3/day to 790 m3/day. Similarly, SGW input to the stream ranged from 891 m3/day to 978 m3/day, while creek seepage ranged from 796 m3/day to 800 m3/day in 2021. In upstream reaches, losing stream conditions were observed in January, June, and September 2020 and January to April 2021, while gaining stream conditions prevailed during other months. Thus, an approximately monthly alternating gaining–losing stream condition was observed in the upstream area. An experimental MT3D transport scenario resulted in an advection–dispersion scenario, showing a cumulative loss of 947 g of NO3-N from SGW to the stream. Denitrification accounted for the cumulative loss of 1406 g of NO3-N from SGW, surpassing 639 g of nitrate from the SGW to the stream during the study period. Additionally, particle tracking using MODPATH indicated a long residence time for SGW nutrients, affirming the efficiency of nitrogen transformation through denitrification. This study is among the first to simulate hydrologic and nutrient interactions in riparian wetlands of a mixed land use catchment in the Appalachian region of the northeastern United States. The results better inform water resource management decisions and modeling efforts in the Appalachian region and similar physiographic regions globally.

A robust lattice Boltzmann scheme for high-throughput predicting effective thermal conductivity of reinforced composites

Accurately predicting effective thermal conductivity is of great importance for the design and performance evaluation of emerging composites. In this paper, an efficient and implementation-friendly lattice Boltzmann (LB) scheme for predicting the effective thermal conductivity of 3D complex structures is proposed. The key innovation is that the optimum convergence parameter of the 3D thermal LB method is found, which enables the LB equation to converge to steady heat conduction equation with the fastest speed and without losing any accuracy. To deal with the thermal contact resistance between different components, an interface treatment scheme is derived. In comparison with the existing schemes, the present scheme enjoys several hundred times higher computational efficiency. By virtue of this LB scheme, the effective thermal conductivity of the reinforced composites with different dimensional fillers are systematically calculated, and a comprehensive machine learning model is developed. This work provides a powerful numerical tool for high-throughput simulations of the 3D representative volume elements with high thermal conductivity ratios and large grid numbers. It may facilitate the application of data-driven techniques in study of the thermal transport properties of emerging composite materials and structures.

Programmable order by disorder effect and underlying phases through dipolar quantum simulators

In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge of the quantum order by disorder effect of the S=1/2 system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of subextensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Among all possible configurations, we focus on the stripe (up and down spins aligning straightly) and kinked (up and down spins forming zigzag spin chains) patterns. Adopting the the real space perturbation theory, we estimate the leading order energy correction when the nearest-neighbor spin exchange coupling, J, is considered, and the overall model becomes an effective XXZ model with a spatial anisotropy. Our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When J becomes larger, we adopt the infinite projected entangled-pair state (iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for two-dimensional quantum simulators. Published by the American Physical Society 2024

3D large deformation modeling of the 2020 Gjerdrum quick clay landslide

A quick clay slide in Gjerdrum, Norway, occurred at 4 a.m. on 30th December 2020, killing ten people and destroying houses, roads, and other infrastructures. Approximately 1.35 million cubic meters of clay were released, a large volume liquefied, and debris was transported almost two kilometers downstream. An investigation following the slide determined that the slide was initialized in a 30-meter-high slope after 2-to-2,5-meter vertical erosion in a small creek running along the toe of the slope. After the initiation, the slide developed retrogressively in the order of 500 meters backward and sideways over a period of about 2 minutes. A conventional geotechnical slope stability analysis explains the initial slide. However, more advanced numerical tools are needed to simulate the retrogressive mechanism and the debris flow. The aim of the paper is to demonstrate a 3D Material Point Method model to capture some of the mechanisms involved from initiation until the debris comes to rest and how this method can be used to reproduce and study the processes involved in large deformation landslides.

Numerical modeling of systems based on SMA wires and pulleys: A finite element formulation within the Arbitrary Lagrangian–Eulerian framework

Thanks to their properties of superelasticity and shape memory effects, SMA wires are often considered for the design of damping devices or actuators coupled to pulleys. In order to dimension such devices for commercialization, it is necessary to develop reliable, robust and fast numerical tools. To this end, simplifying the management of the wire/pulley contact using an Arbitrary Lagrangian–Eulerian (ALE) formulation is an original and effective solution. In this work, the wires are modeled by three-dimensional truss thermo-mechanical finite elements associated with a superelastic law. For each node, the curvilinear abscissa is used as an additional degree of freedom in order to deal with material flow from one element to another. After presenting the ALE formalism and the necessary precautions (advection of variables), as well as the material behavior and thermo-mechanical contact laws at the pulleys, elementary validation tests are studied. Finally, two devices taken from the literature are modeled using the ALE formalism. The results obtained demonstrate the relevance and effectiveness of the approach adopted, as well as the importance of not neglecting friction at the pulleys and thermal effects on the material mechanical response.

Biofuel Concentration in Low-Speed Pre-Ignition in Gasoline Engines

Low-Speed Pre-Ignition (LSPI) is a destructive combustion event associated primarily with new, ultra-efficient, downsized gasoline engines, which provide efficiency benefits in general operation. Biofuels, specifically bio-gasoline, are an alternative fuel that attempts to reduce the harmful emissions output by modern Internal Combustion Engines (ICEs). This study attempts to understand the effect of biofuel use on LSPI, through the use of a numerical simulation tool developed in Ricardo Wave. Development of the tool includes the integration of RFlame, an extension capable of modeling autoignition within a 1D domain. Use of the tool highlights the impact of five ethanol blends, E10, E20, E30, E50 and E85, with clear impacts on both the severity and frequency of LSPI events correlated with chemical properties, such as the enthalpy of vaporization (HoV) and octane number. E30 is highlighted as the critical blend for LSPI severity, with both increased severity and intensity seen with a 30% concentration, and a greater sensitivity to effects such as the start of ignition (SOI). Higher-concentration biofuels, such as E50 and E85 bio-gasoline, show much more favorable behaviors, such as a vast reduction in end-gas knock events, but are limited in their use due to their deployment being both cost-prohibitive and potentially damaging in current hardware. Future work on this topic will surround the further development of the simulation tool to integrate 3D solving elements, understand the role of fluid interactions in LSPI, and study optimal fuel characteristics for future use in ICEs.

Measurement and prediction of the detachment of Aspergillus niger spores in turbulent flows

Aspergillus niger (A. niger) spores can induce numerous health problems. Once the airflow-imposed drag force on an A. niger spore exceeds its binding force with the colony, the spore is detached. Turbulent flow may considerably increase the spore detachment. No method is currently available for prediction of the drag force on a spore and its detachment in turbulent flows. This investigation measured the turbulent velocities and detachment of A. niger colonies in a wind tunnel. Computational fluid dynamics (CFD) was employed to model an A. niger unit subjected to turbulent flow blowing. The top 1 % quantile instantaneous velocity of the turbulent flow was specified as the steady entry flow boundary condition for solving the peak velocity distribution and the peak drag forces onto spores. The predicted spore detachment ratios were compared with the measurement data for model validation. The results revealed that the spore detachment ratios with a turbulence intensity of 17 % to 20 % can be twice to triple the ratio with a turbulence intensity of approximately 1 %, when the average velocity for blowing remains the same. The proposed CFD model can accurately predict the detachment ratios of the A. niger spores. Environmental ImplicationSome people are sensitive to the Aspergillus niger (A. niger) spores, and excessive exposure can cause nasal congestion, skin tingling, coughing, and even asthma. Turbulent flow can considerably increase the spore detachment, due to the increased airflow-imposed drag force on the spores during turbulence. This investigation developed a numerical model to solve for the peak velocity distribution and the peak drag forces onto spores in turbulent flows to predict the spore detachment. With the numerical tool, the airborne fungal spore concentrations would be predictable, which paves a way for intelligent and precise control of fungal aerosol pollution.

Continuous-discontinuous analysis of bench blasting in open-pit mining: Influences of hole packing and caving holes

Bench blasting is commonly used in open-pit mining. Some design parameters such as positions of hole packing and caving holes have great influences on the blasting effects. In this work, with a hybrid discrete-finite element method, numerical simulations of bench blasting are conducted, capturing the whole continuous-discontinuous processes. Considering two engineering cases, the influences of hole packing and caving holes are evaluated. The numerical results not only lead to some improved designs by relocating the packing positions and caving holes but also indicate the reliability of the adopted numerical tools.

Fluvial geomorphic parameters of the Shuiluo River Catchment and their tectonic implications, SE Tibetan Plateau

The Shuiluo River Catchment (SRC) is the front zone of the southeast compression and uplift of the Tibetan Plateau, with intense tectonic activity. In the basin, a series of regional large NW–SE trending active faults are developed. Studying clearly the geomorphic evolution of the SRC is conducive to further understanding the uplift and expansion mechanism of the SE edge of Tibetan Plateau. Our research was based on geographic information system, numerical analysis tool, and digital elevation model data, to extract six geomorpic parameters (hypsometric integral, asymmetry factor, basin shape ratio, valley floor width–valley height ratio, normalized channel steepness index and index of relative active tectonics) in SRC. After eliminating the impacts of climate, catchments area, and glacier, the geomorphic evolution of the SRC is mainly affected by geological structure and differential tectonic uplift movement; in the upstream and midstream (upper part), the shape of valleys and stream longitudinal profile shapes are affected by lithology; affected by geological structure and tectonic uplift, the tectonic activity in the midstream and downstream is relatively strong, and the intensity of activity in the downstream is stronger than that in the midstream, which may suggest that the faults’ activity in the downstream is stronger; the index of relative active tectonics values of the SRC are consistent with the regional seismic intensity, field-work and low-temperature thermochronology which indicates it is reasonable to use the fluvial geomorphic parameters to study the regional geomorphic evolution. The morphological parameters we extracted show different values in different regions of SRC, which may be the result of differential uplift in the southeastern of the Tibetan Plateau.

Effects of Vertical Motion on Uplift of Underground Structure Induced by Soil Liquefaction

The uplift of underground structures induced by soil liquefaction can damage underground structure systems. Numerical simulations have shown that uplift is positively correlated with the energy of horizontal input motion. However, the effects of vertical input motion on uplift have not been studied comprehensively in the past. Previous studies on the vertical motion concluded that the effects of vertical motion on uplift depend on the overall characteristics of earthquake motion. These motion characteristics have only been studied separately in previous studies. A comprehensive study to explore the interactions and overall effects of these characteristics on the uplift of underground structures is essential. In this study, the FLAC program with the PM4Sand model was used as a numerical tool to explore the effects of vertical input motion on the uplift of underground structures. The numerical model was calibrated using centrifuge test results, and 48 earthquake motions were selected as input motions to study the effects of the overall characteristics of earthquake motions on the uplift of underground structures. The simulation results show that the frequency content characteristics of horizontal and vertical motion are the major factors affecting the uplift magnitude and the responses of liquefiable soils. However, most simulation cases show that the inclusion of vertical motion causes a 10% difference in the tunnel uplift, compared to cases without vertical motion.

Innovative coupling of s-stage one-step and spectral methods for non-smooth solutions of nonlinear problems

The behavior of nonlinear dynamical systems arising in mathematical physics through numerical tools is a challenging task for researchers. In this context, an efficient semi-spectral method is proposed and applied to observe the robust solutions for the mathematical physics problems. Firstly, the space variable is approximated by the Vieta-Lucas polynomials and then the s-stage one-step method is applied to discretize the temporal variable which transfers the problem in the form Cn+1=Cn+Δtϕ(x,t,Cn,F(un)). Novel operational matrices of integer order are developed to replace the spatial derivative terms presented in the discussed problem. Related theorems are included in the study to validate the approach mathematically. The proposed semi-spectral schemes convert the considered nonlinear problem to a system of linear algebraic equations which is easier to tackle. We also accomplish an investigation on the error bound and convergence to confirm the mathematical formulation of the computational algorithm. To show the accuracy and effectiveness of the suggested computational method numerous test problems, such as the advection-diffusion problem, generalized Burger-Huxley, sine-Gordon, and modified KdV–Burgers’ equations are considered. An inclusive comparative examination demonstrates the currently suggested computational method in terms of credibility, accuracy, and reliability. Moreover, the coupling of the spectral method with the fourth-order Runge-Kutta method seems outstanding to handle the nonlinear problem to examine the precise smooth and non-smooth solutions of physical problems. The computational order of convergence (COC) is computed numerically through numerous simulations of the proposed schemes. It is found that the proposed schemes are in exponential order of convergence in the spatial direction and the COC in the temporal direction validates the studies in the literature.

Shock–shock interaction on the Reusability Flight Experiment (ReFEx)

AbstractThe Reusability Flight Experiment (ReFEx) is currently under development at the German Aerospace Center (DLR). A coupled experimental and numerical campaign was carried out to investigate the surface heating on the payload geometry during return consisting of a forebody and canard. In this way, numerical tools for a post-flight analysis can be preemptively improved where required. Experiments were undertaken at the High Enthalpy Shock Tunnel Göttingen (HEG) on a 1:4 scale model with the use of temperature sensitive paint on the payload geometry to obtain surface heat flux. The model configuration was varied in angle of attack and canard deflection. Laminar and turbulence-model solvers in the DLR-TAU code were used for the numerical simulations. This investigation focussed on the shock–shock interaction of the nose bow shock with the leading-edge shock of the canards showing significant surface heat flux along the canard. Larger surface heat fluxes were measured in the experiments downstream of the shock interaction on the canard, than obtained from the laminar CFD calculations. This was attributed to transition of the boundary layer within the interaction regions, in the presence of significant adverse pressure gradients. Other flow features along the forebody in the vicinity of the canard were qualitatively matched better by the fully-turbulent numerical solutions than the laminar ones. This work aims to demonstrate the extent to which the numerical and experimental tools assist useful insights into flow phenomena during the return stages of the ReFEx payload geometry, and the aspects for which improvements are required.

Tactile Sensing and Grasping Through Thin‐Shell Buckling

Soft and lightweight grippers have greatly enhanced the performance of robotic manipulators in handling complex objects with varying shape, texture, and stiffness. However, the combination of universal grasping with passive sensing capabilities still presents challenges. To overcome this limitation, a fluidic soft gripper is introduced based on the buckling of soft, thin hemispherical shells. Leveraging a single fluidic pressure input, the soft gripper can grasp slippery and delicate objects while passively providing information on this physical interaction. Guided by analytical, numerical, and experimental tools, the novel grasping principle of this mechanics‐based soft gripper is explored. First, the buckling behavior of a free hemisphere is characterized as a function of its geometric parameters. Inspired by the free hemisphere's two‐lobe mode shape ideal for grasping purposes, it is demonstrated that the gripper can perform dexterous manipulation and gentle gripping of fragile objects in confined spaces and underwater environments. Last, the soft gripper's embedded capability of detecting contact, grasping, and release conditions during the interaction with an unknown object is proved. This simple buckling‐based soft gripper opens new avenues for the design of adaptive gripper morphologies with tactile sensing capabilities for applications ranging from medical and agricultural robotics to space and underwater exploration.

Optimization of machining path for integral impeller side milling based on SA-PSO fusion algorithm in CNC machine tools

The five axis linkage Computer Numerical Control machine tool for integral impeller can achieve blade machining through side milling, which is of great significance for improving the machining accuracy, production efficiency, and long-term stability of integral impeller blades. This study is based on non-uniform rational B-spline curves and aims to reduce the surface over cutting or under cutting of integral turbine blades. The path planning of non deployable ruled surfaces was analyzed in depth through side milling, and the path planning model of the side milling cutter axis was solved through a fusion algorithm of simulated annealing algorithm and particle swarm optimization algorithm, in order to find the optimal path through iterative process. As the number of iterations increased, the error values of particle swarm optimization algorithm and simulated annealing particle swarm optimization fusion algorithm gradually decreased, with convergence times of about 7 and 6, respectively. The stable error value of the fusion algorithm was 0.253, which is 30.45% lower than that of the particle swarm optimization algorithm. The optimal number of iterations for solving the model using particle swarm optimization algorithm and fusion algorithm was the 7th, with range values of 0.0213 and 0.0165 mm, respectively. The tool axis trajectory surface optimized by the fusion algorithm was closer to the tool axis motion state compared to the initial tool axis trajectory surface. The range of the sum of mean squared deviations for single and global cutting was 0.0011–0.0198 and 0.046–0.0341, but the overall error value was relatively small. This study effectively reduces the envelope error of machining tools and improves machining accuracy, thereby solving the principle error of non expandable ruled surfaces in the motion trajectory of the blade axis of the integral turbine. This provides new research ideas for the intelligent development of Computer Numerical Control machining technology.

Onset of thermal convection in a solid spherical shell with melting at either or both boundaries

SUMMARY Thermal convection in planetary solid (rocky or icy) mantles sometimes occurs adjacent to liquid layers with a phase equilibrium at the boundary. The possibility of a solid–liquid phase change at the boundary has been shown to greatly help convection in the solid layer in spheres and plane layers and a similar study is performed here for a spherical shell with a radius-independent central gravity subject to a destabilizing temperature difference. The solid–liquid phase change is considered as a mechanical boundary condition and applies at either or both horizontal boundaries. The boundary condition is controlled by a phase change number, Φ, that compares the timescale for latent heat exchange in the liquid side to that necessary to build a topography at the boundary. We introduce a numerical tool, available at https://github.com/amorison/stablinrb, to carry out the linear stability analysis of the studied setup as well as other similar situations (Cartesian geometry, arbitrary temperature and viscosity depth-dependent profiles). Decreasing Φ makes the phase change more efficient, which reduces the importance of viscous resistance associated to the boundary and makes the critical Rayleigh number for the onset of convection smaller and the wavelength of the critical mode larger, for all values of the radii ratio, γ. In particular, for a phase change boundary condition at the top or at both boundaries, the mode with a spherical harmonics degree of 1 is always favoured for Φ ≲ 10−1. Such a mode is also favoured for a phase change at the bottom boundary for small (γ ≲ 0.45) or large (γ ≳ 0.75) radii ratio. Such dynamics could help explaining the hemispherical dichotomy observed in the structure of many planetary objects.

Development of a multi-layer green-ampt infiltration based modeling framework for hydrologic process simulation and design of various low impact development measures for mitigating urban flooding

ABSTRACT Low Impact Development (LID) measures have proven to be effective in reducing the runoff volume and the peak of runoff at small spatial scales. Assessment of the hydrological impacts of LID measures at river basin scales is currently limited by the absence of adequate physically-based process models that can simulate LID processes at such scales. In this study, an attempt has been made to develop LID modules to simulate the water balance and hydrological processes based on the Multi-Layer Green-Ampt (MLGA) infiltration method, which is an advancement to the existing LID modeling techniques. The performance of the MLGA-based LID modules was benchmarked with the process-intensive numerical tool HYDRUS 1D for about 5000 soil samples across the soil textural classes. The results indicated that the MLGA-based model simulates the hydrological processes in close agreement with HYDRUS for soils with moderate-to-high hydraulic conductivity values, which are amenable for LID implementation.

Buckling analysis of thin-walled laminated composite or functionally graded sandwich I-beams using a refined beam theory

This study presents the buckling and lateral torsional buckling behaviors of thin-walled laminated composite or functionally graded sandwich I-beams. A refined beam model (RBT) based on the 3D Saint-Venant (SV) solution is used in this study to formulate the problem. This model allows for a realistic analysis of beams with arbitrary cross-sections and is free from the limitations of classical beam theories. The displacement models establish a consistent 1D beam theory that accurately captures the essence of the cross-section’s nature. The governing models consider cross-section deformations, including in and out of plane warpings and distortions derived from the 3D SV solution associated with the cross-section vibrational behavior. Furthermore, a user-friendly numerical tool called CSB (cross-section and beam analysis) is used to facilitate the implementation of this method. The numerical results are examined in detail and compared with previous works to investigate the influence of boundary conditions, angle-ply, shear effects, span-to-height ratio, and material distribution on the critical buckling loads of thin-walled I-beams. The results demonstrate that the RBT models accurately and efficiently analyze thin-walled I-beams under different loads and boundary conditions. Furthermore, some of the new results are presented as reference values for the future.